From the looks of it it's just oscillation caused by breathing in certain ways, so yes, part of the autonomic nervous system, rather than something the cat choo

From the looks of it it's just oscillation caused by breathing in certain ways, so yes, part of the autonomic nervous system, rather than something the cat chooses to do. The wording makes it sound like this is not all purring though, so there may be other ways cats can conciously choose to purr.